Abstract
We classify all positive n-particle NkMHV Yangian invariants in \( \mathcal{N} \) = 4 YangMills theory with n = 5k, which we call extremal because none exist for n > 5k. We show that this problem is equivalent to that of enumerating plane cactus graphs with k pentagons. We use the known solution of that problem to provide an exact expression for the number of cyclic classes of such invariants for any k, and a simple rule for writing them down explicitly. We provide an alternative (but equivalent) classification by showing that a product of k five-brackets with disjoint sets of indices is a positive Yangian invariant if and only if the sets are all weakly separated.
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Lippstreu, L., Mago, J., Spradlin, M. et al. Weak separation, positivity and extremal Yangian invariants. J. High Energ. Phys. 2019, 93 (2019). https://doi.org/10.1007/JHEP09(2019)093
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DOI: https://doi.org/10.1007/JHEP09(2019)093